Definition: Amazake literally means sweet sake, but it's not actually sake. It's a thick drink which is traditionally made by allowing a mixture of steamed rice and rice koji to ferment at about 60 degrees C for about 8-12 hours. It's naturally sweet and contains almost no alcohol.
Amazake can be simply made with sake kasu (sake lees), which is a byproduct of sake making. Mix water and some sake kasu to preferred thickness in a sauce pan. Then, simmer and season with some sugar. This type of amazake contains some alcohol.